Answer:
Since, \[x+\frac{1}{x}=5\] Squaring on both sides, \[{{\left( x+\frac{1}{x} \right)}^{2}}={{5}^{2}}\] or \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2\times x\times \frac{1}{x}={{(5)}^{2}}\] or \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2=25\] or \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=25-2\] or \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=23\]
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